Algorithmic independence of initial condition and dynamical law in thermodynamics and causal inference

TL;DR

This paper proposes a principle linking the initial condition's algorithmic independence from dynamical laws to thermodynamics and causal inference, explaining temporal asymmetry and causal asymmetry in probabilistic terms.

Contribution

It introduces a unifying principle that connects thermodynamic arrow of time with causal inference asymmetries through algorithmic independence.

Findings

Initial conditions are typically algorithmically independent of dynamical laws.

This independence explains the thermodynamic arrow of time.

It provides a theoretical basis for causal asymmetries in probability distributions.

Abstract

We postulate a principle stating that the initial condition of a physical system is typically algorithmically independent of the dynamical law. We argue that this links thermodynamics and causal inference. On the one hand, it entails behaviour that is similar to the usual arrow of time. On the other hand, it motivates a statistical asymmetry between cause and effect that has recently postulated in the field of causal inference, namely, that the probability distribution P(cause) contains no information about the conditional distribution P(effect|cause) and vice versa, while P(effect) may contain information about P(cause|effect).